Common Emitter Gain question

I have a circuit that I understand the DC gain, but I don't understand the AC gain.

the top resistor on the base from Vcc is 18k, bottom is 18.2k into a 2n3904 with an Re of 562 and an Re of 1k, vcc is 9v.

There is a cap in parallel with Re that is 100uf and my input freq. is 1kHz.

The DC gain should be Rc/Re which is a little less than 2. But when I scope the input and the output, it's like 100 times.

I understand that cap is bypassing all the AC to ground, but why the higher gain?

I tried that and my gain is like 629 when my gain is clearly 100 because I'm looking at the input which is 1mV rms and my output is approx. 100mV rms.

Sorry, it was obviously more complex than my simplistic approach. I'll dig out my old text books if no-One provides an answer. I know that ac gain in common emitters was something that was done to death on a few of my courses in analogue electronics. Strange really, I seem to have spent the whole of my career without having needed the theory once :-)

HN

do you have a load resistance? if so it parallels Rc

dont forget about the resistance in the emitter junction (r ej). its small but adds in series to the ac resistance.

Maximum common emmiter gain is 40 X Vcc

That occurs near saturati>

I don't think it's 40 x Vcc

I think what I was missing was that I needed to include re' in the equation too and also consider the resistors on the base of the transistor (r1 and r2)

re depends on the current flowing' At 1 Ma it is about 25 ohms. The value of 40 Vcc is for a grounded emmitter configureation Close to saturation the current is limited by Rc. This means that as Rc gets bigger the current drops and re also gets bigger in proportion to Rc. Because they track, both drop out of the equation and the gain is 40Vcc. If there is a substantial externam emmitter resistance which is a lot bigger than re than the gain is Rc over Re. If Re is not a lot bigger than re then the effects of re must be considered, but remember re is a moving target varying with current. and the gain varies with the current flowing.